Virtual Work Method on a Truss

[dtb_419]

Homework Statement

I want to calculate the horizontal deflections at joints A and F (using Virtual Work method taught in Structural Engineering). Cross-Sectional Area (A) and E values are provided in the problem, and the attachment has all relevant dimensions and applied loads.

Homework Equations

Deflection is 1[k](Δ)=∑(Virtual Force/AE)

The Attempt at a Solution

So far in class, Virtual Work problems have involved using the Unit Load Method (a hypothetical 1 kip load that can be used to calculate deflection from its effect on a given structure).

The general method (as I understand it, in a truss structure) is this:

1. Solve all member forces.

2. Organize all information (member length in inches, member force, cross-sec area, and MEMBER FORCE FROM UNIT LOADING into a table.

3. Summation of Virtual Forces from table plugged into Deflection Equation from Virtual Work.

Step 1. I've already done myself (joint method), and Step 3. is a matter of plugging in known data from Step 2. No questions there.

Step 2. is where my question is.

This particular question wants horizontal deflections at A and also F. What I think I should do is introduce a horizontal 1 kip load at each of the respective joints, and repeat the joint analysis to reflect this change from the unit load. But in what direction (sign convention) should they be introduced? Should I introduce a horizontal 1 kip load at EACH joint, or only the requested joints?

Some problems I've seen introduce the unit load at only the requested joint, and recalculate all other member forces to adjust for that change (which is what I'm leaning towards doing), but others introduce the unit load immediately, without taking initial member forces. This is confusing, and so I'm asking for a clarification in procedure.

No numbers are necessary. Thanks everyone!

 

[pongo38]

If you want the deflection at a particular point, apply the unit load there, and only there. The direction doesn't really matter, but if the answer is negative, that means it was the other way. Still correct though. So you have the frame analyzed with the given loads, and secondly, you have the frame analyzed with just the unit load. Do you know how to combine these two results to give you the deflection you want?

 

[dtb_419]

pongo38, thanks for your reply!

Regarding the two results for deflection of A and F, aren't they separate deflections? Like, for A I apply a unit load at A horizontally, and calculate changes in member forces, and multiply in the PL/AE equation eventually? Then do the same thing for F, and have two separate deflections?

I thought that for however many deflections you wanted, you had to have that many virtual structures? Are you saying that I apply a unit load to the truss at A and F at the same time?

 

[pongo38]

Not at the same time. Two separate processes, one for each deflection required. However, there is a matrix method that does it all in one go. But that is not the method you are pursuing here.

 

[rezeew]

I would recommend using the virtual work method to calculate the horizontal deflections at joints A and F. This method is commonly used in structural engineering and can provide accurate results when applied correctly.

In terms of the specific problem, it is important to carefully organize all the information and data, including member forces, cross-sectional area, and applied loads. This will help in accurately calculating the deflections at the requested joints.

In terms of introducing the horizontal 1 kip load, it is important to follow a consistent sign convention. This means that the load should be introduced in the same direction at both joints A and F. Additionally, it is important to consider the effect of the load on all other member forces, not just at the requested joints. This will ensure that the calculations are accurate and take into account all relevant factors.

In summary, I would recommend carefully organizing the information and using a consistent sign convention when introducing the horizontal 1 kip load. Additionally, it is important to consider the effect of the load on all member forces in order to accurately calculate the deflections at joints A and F.